1. Field of the Invention (Technical Field)
Embodiments of the present invention relate to a method, system, and/or technique for detecting the formation of the Brillouin precursor waveforms produced by the propagation of any transmitted signal through a dispersive media. Embodiments of the present invention also relate to a method, system, and/or technique, to process evolving Brillouin precursors as a result of an EM wave propagating through dispersive media, such as soil, foliage, water, walls, and human tissues at microwave frequencies.
2. Description of Related Art
The propagation of electromagnetic (EM) waves through a linear, temporally dispersive medium is a classic, on-going problem. It has assumed significant importance in the recent past, particularly, for systems operating with EM pulses of extremely short duration and/or of ultrawideband (UWB) frequency spectrum; the UWB spectrum is needed for finer range resolution in imaging systems, and for higher data rates in communication. The earliest research on the subject appears to have originated in or around the earlier part of the nineteenth century by various researchers working on the phenomenon of dispersion of light. Subsequently, a study around the year 1914 indicated the formation of “forerunners” or “precursors” arising out of electromagnetic (EM) propagating waves in dispersive media. The first and the second of these forerunners are also now known as the Sommerfeld, and the Brillouin precursors, respectively. The theory related to these waveforms could not be further understood and applied due to the intractable nature of the mathematics governing these waveforms. In dispersive media, each frequency component travels with its own phase velocity and undergoes a different absorption rate. These two effects determine the structure of the propagating fields at a given distance into the medium, resulting in fields called precursors.
In 1969, one of the first studies to demonstrate the existence of the precursors at RF and Microwave frequencies was conducted in a waveguide, P. Pleshko, I. Palózc, “Experimental observation of Sommerfeld and Brillouin precursors in the microwave domain”, Physical Review Letters, vol. 22, issue 22, Jun. 1969. It is apparently the only one to refer to the observed transient response as precursors. The conditions in under which that data was obtained were very restrictive and particular. For example, it was conducted in an air-filled waveguide and measured in the frequency region wherein the phase and attenuation constants show a dispersive behavior. This situation represents a virtual dispersive material and not a physical material. This situation represents a virtual dispersive material and not a physical material. Remaining published experimental work are related to optical frequencies, and they involve measurements in mercury, optical fibers, and other systems not valid for microwave UWB bands.
In the more recent past, asymptotic analysis has provided an approximate closed-form solution for an otherwise largely intractable mathematical problem. The asymptotic analysis has analytically shown the influence of Brillouin precursors on signal arrival and pulse distortion in dispersive media, concluding that Brillouin precursors become a predominant component at depths greater than one absorption depth at the carrier frequency of the signal. In brief, the Brillouin precursor is characterized by (a) algebraically attenuating peak amplitude with propagation distance z (i.e. signal strength proportional to z−k, k being a medium-dependent constant) compared to that e−αf(0)-z of the exponentially decaying EM field at the carrier frequency f0; and (b) the center of the spectrum of the precursor downshifts with propagation distance z.
That analysis, however, was limited to theoretical investigations only. It could not yet be used in any experimental system operating at Radio Frequency (RF) and Microwave frequencies, because: (1) non-familiarity of various researchers with the concept of precursors; (2) not very many researchers are working in this area because of (1); (3) efforts in the past to observe these waveforms experimentally were not successful, thereby restricting this field to simulations only, particularly at RF and Microwave bands; and (4) non-availability of methods and techniques to demonstrate the practical existence of these waveforms at RF and Microwave regions.
The other published experimental works such as K. E. Oughstun and G. C. Sherman. Electromagnetic and Optical Pulse Propagation, Volume 2. Ed. Berlin, Germany: Springer-Verlag, 2009, pages 656-669, are limited to optical frequencies, and they involve measurements in mercury, optical fibers, and other systems not valid for the microwave band. The experimental detection of precursor waveforms at RF and microwave frequencies is of utmost importance since these frequencies are commonly used in numerous applications where optical frequencies do not provide desirable results. Additionally, the known experimental approaches are based on measurements performed in the time domain, thus making their implementation difficult due to the more complex instrumentation which is required. Additionally, in the time domain approach, the experimental observation of the Brillouin precursor must be repeated for each different pulse. This extends the time needed, and therefore the measurement conditions can suffer from conditional deviations, such as slight changes in temperature, humidity, and salinity of the material, thus providing less accurate results because such variables can influence the electrical conductivity of the dispersive material, σ0 [S/m], thereby producing different and non-consistent results.
The received pulses are usually processed by a dispersion compensation filter that tries to cancel the frequency dispersion introduced by propagation through a dispersive media. But these filters do not fully compensate the dispersion phenomena, specially the formation of Brillouin precursors, or forerunners, that leads to the pulse spreading effect. This effect increases the range uncertainty radar feature if an application through or on dispersive media is attempted. Accordingly, this temporal width always exists and depends exclusively of the material intrinsic parameters. If digital waveforms are used in transmission, some classical reception filter techniques, such as matched filters, encounter this uncertainty because of the broadening suffered by the transmitted pulses. There is thus a need for a method, apparatus, and system capable of analyzing the formation of these forerunners to achieve an optimum design of receiver structures to mitigate the undesired impairment and ensuring a minimum distortion reception in the frame of Ultra-wide Band (“UWB”) radar.
Very few experimental studies have been reported in the literature to experimentally detect, process, and analyze precursors at microwave frequencies. In “Experimental observation of Sommerfeld and Brillouin precursors in the microwave domain”, Physical Review Letters, 1969, 22, (22), pp. 1201-1204, Pleshko, P., and Palózc, I., conducted an experiment using an air-filled waveguide in the vicinity of a cutoff frequency representing a virtual dispersive material and not a physical material.
U.S. Pat. No. 6,429,801 discloses the use of precursor waveforms. However, it cannot be adopted readily for various applications because it involves just one kind of pulse which requires to divide the sine carrier modulated pulse and both divided signals are phase modulated to produce the phase reversal so as the precursor is formed on the signal to be transmitted. The target application of that approach is to determine the possible material properties associated with the object detected by the radar. That approach also limits the transmit power of the GPR system in which it is intended to be used and thus, restricting the overall dynamic range of the system. Further, that approach is based on an impulse radar technology, requiring specialized hardware to generate well-defined pulses with a sharp rise and fall time. Its utility is thus further limited in typical radar applications due to the power and signal constraints. Additionally, the invention by U.S. Pat. No. 6,429,801 does not mention explicitly that the formed precursor is the Brillouin precursor; it identifies transient signals as first and second precursors.
However, up to present, despite of the evident advantages, the study of this phenomenon has been constrained by the inexistence of a reliable method valid to detect its formation in actual media.